# Tagged Questions

The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.

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### what is the argument for not using the average of an average?

I want to disprove someone's calculation of percentage of cash sales for a year by taking summing percentage of cash sales by month and dividing by 12. I sense the correct way is to take total cash ...
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### Average Distance Between Random Points in a Rectangle

My question is similar to this one but for rectangles instead of lines. Suppose I have a rectangle with sides of length $L_w$ and $L_h$. What is the average distance between two uniformly-distributed ...
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### Average $lcm(a,b)$, $1\le a \le b \le n$, and asymptotic behavior

What is the average value for $\mathrm{lcm}(a,b)$, with $1\le a \le b \le n$, for a given $n$, and what is the asymptotic behavior? The $\mathrm{lcm}$ is the least common multiple. I have ...
7k views

### Calculate average wind direction

What is the best way to average wind direction? I have found many conflicting suggestions elsewhere. Best one I saw is to average SINs of all angles in radians and take inverse SIN of the result. ...
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### What is the name of this type of “average”?

Given two variables $x$ and $y$, $$\frac{2}{1/x + 1/y}$$ looks like some kind of average of $x$ and $y$. Is there a name for it? Where can i look up more information (such as properties) of this ...
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### Average Number of Roots of a Polynomial modulo p

Let $f \in \mathbb{Z}[X]$ be an irreducible non-constant polynomial, and consider this polynomial modulo $p$ for each prime $p$. On average, how many roots does $f$ have modulo $p$? I.e., if $r(p)$ ...
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### Dirichlet Series and Average Values of Certain Arithmetic Functions

If an arithmetic function $f(n)$ has Dirichlet series $\zeta(s) \prod_{i,j = 1} \frac{\zeta(a_i s)}{\zeta(b_j s)}$, for which values of $a_{i}$ and $b_{j}$ is the following true? That \begin{align} \...
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### Mean value of the rotation angle is 126.5°

In the paper "Applications of Quaternions to Computation with Rotations" by Eugene Salamin, 1979 (click here), they get 126.5 degrees as the mean value of the rotation angle of a random rotation (by ...
12k views

### Standard deviation of the weighted mean [duplicate]

How do you find the standard deviation of the weighted mean? The weighted mean is defined: $\bar{x}_w = \frac{\sum{wx}}{\sum{w}}$ The weighted standard deviation (since it is not specified, I take ...
457 views

### Average transformation matrix?

I have several estimates of the transformation matrix between two planes and some values that give some indication of the error involved in the estimate. How can I use this information to gain the ...
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### If $\sum\limits_{k=1}^n y_k\geq n$ and $\sum\limits_{k=1}^n \frac{1}{y_k}\geq n$, then $\prod\limits_{k=1}^n y_k\geq 1$?

Let $y_1,\ldots y_n$ be positive real numbers satisfying $y_1+\cdots+y_n\geq n$ and $\displaystyle{\frac{1}{y_1}+\cdots+\frac{1}{y_n}\geq n}$. Is it true that $y_1y_2\cdots y_n\geq 1$?
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### Average value of $e^{-x}$ from $0$ to $\infty$

I just signed up for this site so I hope I'm doing this right. I've been having trouble wrapping my head around the average value of the function $e^{-x}$ from 0 to $\infty$. I know that the average ...
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### In what sense is the “average” of $sin(x)$ equal to 0?

I think it makes intuitive sense that if a phenomenon is described by simple sinusoidal oscillation, it is "on average" equal to its midrange, but I think I failed in trying to make that statement ...
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### Definition of random

Suppose that you has to guess given a set of numbers If they are random. The mathematical expectation Is there a definition of randomness that allow this prove/test? Is even possible? if so: How ...
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### The Exponential decay.

I am studying semiconductor physics. there is a paragraph about Drude model in E.spenke's book "Electronic semiconductors" page 259 in art §9: "if on the average, a time $τ$ elapses between two ...
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### Is the norm of the average $\le$ the norm of the max?

Given $\pmb X \in \mathcal{R}^p$, denote the elements of $\pmb X$ as $\pmb x_i$ for $i= 1, \dots, n$. Denote the $t(\pmb X)$ as the average of $\pmb X$ \pmb t(\pmb X) = \frac 1 n \...
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### How do I average a new number into an established percentage if I know the number of items?

This seems like something I should be able to do but I can not for the life of me figure it out. I'm writing a program to calculate an average score; let's say that my data looks like this. x = ...
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### Course Grade - Statistics Question

I'm confused about finding the standard deviation of various weighted objects in a problem. For example, consider an academic setting, with four assessments as follows: ...
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### leading and lagging moving average indicator

What are leading short and lagging long moving average indicators and how do we calculate them? e.g. for the following data set, and let window size be 2. Can you ...
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### Determine drug concentration over time, given its halflife and dosage

I want to calculate which of two doses is going to have the most active ingredient over the total time of an experiment. So as an example let's say I have a drug which has a halflife of 5 hours, and ...
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### what does ensemble average mean?

I'm studying this paper and somewhere in the conclusion part is written: "Since this rotation of the coherency matrix is carried out based on the ensemble average of polarimetric scattering ...
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### What is the maximum value of the sum $\sum_{i=1}^L(\bar{x}-x_i)$, in this specific case.

Let $x_i$ be a positive real variable, with $i=1,2,...,K$. We denote by $\bar{x}$ the average value of the values $x_1, x_2,...,x_K$. Let $a=\min_i x_i$ and $b=\max_i x_i$, then $x_i \in [a,b]$. My ...
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### What is this average called?

What is this average called? I tried Googling it but couldn't find anything about it. It's something between an arithmetic mean and a geometric mean, by which I mean you iterate both averages for two ...
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### How to find the function $f$ that satisfies $f(x, y) = f(x^{-1}, y^{-1})^{-1}$ and $f(x, y)$ is $\approx$ $average(x, y)$?

Fist of all, I'm a programmer, not a mathematician, and I'm sorry for my non native English. And I'm sorry if the question is not appropriate, it is my first time here. Or if the question has no ...
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### Simplified Averages - Always true?

While working on an "average rating" function for a website, I came across an idea for simplified averages, but I want to confirm that it always works. If it does, I might be able to keep a running ...
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### What do curly brackets mean in this formula?

In this paper, in the Formula at the beginning of 2.2, we have $B=\{b_i(O_t)\}$ where $i=0,1$ - the number of probability formula $O_t$ - the state at moment $t$ $b_i(O_t)$ - two probabilities ...
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### Expected value (mean) of function from polyline

Suppose we have a polyline that has such properties: It consists of n segments First segment's ends are (0, 0) and ...
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### Finding a summarizing vector for average angle calculation

Let $L$ and $R$ be two bags of positive vectors such that all vectors have length $k$. Define the distance $d_{avg}$ between the bags as the average pairwise angle between the vectors. Is is possible ...
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### Find spikes in data

I have some datasets and I need to find spikes in them. Imagine the data looks like trading data. If the spike is big enough, I need to log it, otherwise, proceed in the analysis. I tried with a ...
I came across the following question. A man travels a distance of $20$ miles at $60$ miles/hr and then return over the same route at $40$ miles/hr. What is the average rate for the round trip in ...